Solve each equation for x. (Enter an exact answer.) (a) 2x − 7 = 5
remember you can do anythingn to an equaiton aslong as you do it to both sides
2x-7=5
add 7 to both sides
2x+7-7=5+7
2x+0=12
2x=12
divide both sides by 2
2x/2=12/2
1x=6
x=6
some new info says the quesiton is
2^x-7=5
dont forget
\(log_a(bc)=(log_a(b))(log_a(c))\) and
\(log_a(a^x)=x\)
add 7 to both sideds
2^x=12
take the log₂ of both sides
log₂(2^x)=log₂(12)
x=log₂(12)
log₂(12)=(log₂(4)(log₂(3))=(log₂(2^2))(log₂(3))=(2log₂(2))(log₂(3))=2log₂(3)
x=2log₂(3